1 /* Functions to make fuzzy comparisons between strings
2 Copyright (C) 1988-1989, 1992-1993, 1995, 2001-2003, 2006, 2008
3 Free Software Foundation, Inc.
5 This program is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation; either version 3 of the License, or
8 (at your option) any later version.
10 This program is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
19 Derived from GNU diff 2.7, analyze.c et al.
21 The basic idea is to consider two vectors as similar if, when
22 transforming the first vector into the second vector through a
23 sequence of edits (inserts and deletes of one element each),
24 this sequence is short - or equivalently, if the ordered list
25 of elements that are untouched by these edits is long. For a
26 good introduction to the subject, read about the "Levenshtein
27 distance" in Wikipedia.
29 The basic algorithm is described in:
30 "An O(ND) Difference Algorithm and its Variations", Eugene Myers,
31 Algorithmica Vol. 1 No. 2, 1986, pp. 251-266;
32 see especially section 4.2, which describes the variation used below.
34 The basic algorithm was independently discovered as described in:
35 "Algorithms for Approximate String Matching", E. Ukkonen,
36 Information and Control Vol. 64, 1985, pp. 100-118.
38 Unless the 'find_minimal' flag is set, this code uses the TOO_EXPENSIVE
39 heuristic, by Paul Eggert, to limit the cost to O(N**1.5 log N)
40 at the price of producing suboptimal output for large inputs with
54 #include "glthread/lock.h"
55 #include "glthread/tls.h"
60 # define uintptr_t unsigned long
65 #define EQUAL(x,y) ((x) == (y))
67 #define EXTRA_CONTEXT_FIELDS \
68 /* The number of edits beyond which the computation can be aborted. */ \
69 int edit_count_limit; \
70 /* The number of edits (= number of elements inserted, plus the number of \
71 elements deleted), temporarily minus edit_count_limit. */ \
73 #define NOTE_DELETE(ctxt, xoff) ctxt->edit_count++
74 #define NOTE_INSERT(ctxt, yoff) ctxt->edit_count++
75 #define EARLY_ABORT(ctxt) ctxt->edit_count > 0
76 /* We don't need USE_HEURISTIC, since it is unlikely in typical uses of
81 /* Because fstrcmp is typically called multiple times, attempt to minimize
82 the number of memory allocations performed. Thus, let a call reuse the
83 memory already allocated by the previous call, if it is sufficient.
84 To make it multithread-safe, without need for a lock that protects the
85 already allocated memory, store the allocated memory per thread. Free
86 it only when the thread exits. */
88 static gl_tls_key_t buffer_key; /* TLS key for a 'int *' */
89 static gl_tls_key_t bufmax_key; /* TLS key for a 'size_t' */
94 gl_tls_key_init (buffer_key, free);
95 gl_tls_key_init (bufmax_key, NULL);
96 /* The per-thread initial values are NULL and 0, respectively. */
99 /* Ensure that keys_init is called once only. */
100 gl_once_define(static, keys_init_once)
104 fstrcmp_bounded (const char *string1, const char *string2, double lower_bound)
107 int xvec_length = strlen (string1);
108 int yvec_length = strlen (string2);
115 /* short-circuit obvious comparisons */
116 if (xvec_length == 0 || yvec_length == 0)
117 return (xvec_length == 0 && yvec_length == 0 ? 1.0 : 0.0);
121 /* Compute a quick upper bound.
122 Each edit is an insertion or deletion of an element, hence modifies
123 the length of the sequence by at most 1.
124 Therefore, when starting from a sequence X and ending at a sequence Y,
125 with N edits, | yvec_length - xvec_length | <= N. (Proof by
127 So, at the end, we will have
128 edit_count >= | xvec_length - yvec_length |.
131 = (xvec_length + yvec_length - edit_count)
132 / (xvec_length + yvec_length)
133 <= (xvec_length + yvec_length - | yvec_length - xvec_length |)
134 / (xvec_length + yvec_length)
135 = 2 * min (xvec_length, yvec_length) / (xvec_length + yvec_length).
137 volatile double upper_bound =
138 (double) (2 * MIN (xvec_length, yvec_length))
139 / (xvec_length + yvec_length);
141 if (upper_bound < lower_bound)
142 /* Return an arbitrary value < LOWER_BOUND. */
146 /* When X and Y are both small, avoid the overhead of setting up an
147 array of size 256. */
148 if (xvec_length + yvec_length >= 20)
150 /* Compute a less quick upper bound.
151 Each edit is an insertion or deletion of a character, hence
152 modifies the occurrence count of a character by 1 and leaves the
153 other occurrence counts unchanged.
154 Therefore, when starting from a sequence X and ending at a
155 sequence Y, and denoting the occurrence count of C in X with
156 OCC (X, C), with N edits,
157 sum_C | OCC (X, C) - OCC (Y, C) | <= N.
158 (Proof by induction over N.)
159 So, at the end, we will have
160 edit_count >= sum_C | OCC (X, C) - OCC (Y, C) |,
163 = (xvec_length + yvec_length - edit_count)
164 / (xvec_length + yvec_length)
165 <= (xvec_length + yvec_length - sum_C | OCC(X,C) - OCC(Y,C) |)
166 / (xvec_length + yvec_length).
168 int occ_diff[UCHAR_MAX + 1]; /* array C -> OCC(X,C) - OCC(Y,C) */
171 /* Determine the occurrence counts in X. */
172 memset (occ_diff, 0, sizeof (occ_diff));
173 for (i = xvec_length - 1; i >= 0; i--)
174 occ_diff[(unsigned char) string1[i]]++;
175 /* Subtract the occurrence counts in Y. */
176 for (i = yvec_length - 1; i >= 0; i--)
177 occ_diff[(unsigned char) string2[i]]--;
178 /* Sum up the absolute values. */
180 for (i = 0; i <= UCHAR_MAX; i++)
183 sum += (d >= 0 ? d : -d);
186 upper_bound = 1.0 - (double) sum / (xvec_length + yvec_length);
188 if (upper_bound < lower_bound)
189 /* Return an arbitrary value < LOWER_BOUND. */
195 /* set the info for each string. */
199 /* Set TOO_EXPENSIVE to be approximate square root of input size,
200 bounded below by 256. */
201 ctxt.too_expensive = 1;
202 for (i = xvec_length + yvec_length;
205 ctxt.too_expensive <<= 1;
206 if (ctxt.too_expensive < 256)
207 ctxt.too_expensive = 256;
209 /* Allocate memory for fdiag and bdiag from a thread-local pool. */
210 fdiag_len = xvec_length + yvec_length + 3;
211 gl_once (keys_init_once, keys_init);
212 buffer = (int *) gl_tls_get (buffer_key);
213 bufmax = (size_t) (uintptr_t) gl_tls_get (bufmax_key);
214 if (fdiag_len > bufmax)
216 /* Need more memory. */
218 if (fdiag_len > bufmax)
220 /* Calling xrealloc would be a waste: buffer's contents does not need
224 buffer = (int *) xnmalloc (bufmax, 2 * sizeof (int));
225 gl_tls_set (buffer_key, buffer);
226 gl_tls_set (bufmax_key, (void *) (uintptr_t) bufmax);
228 ctxt.fdiag = buffer + yvec_length + 1;
229 ctxt.bdiag = ctxt.fdiag + fdiag_len;
231 /* The edit_count is only ever increased. The computation can be aborted
233 (xvec_length + yvec_length - edit_count) / (xvec_length + yvec_length)
236 edit_count > (xvec_length + yvec_length) * (1 - lower_bound)
238 edit_count > floor((xvec_length + yvec_length) * (1 - lower_bound)).
239 We need to add an epsilon inside the floor(...) argument, to neutralize
241 ctxt.edit_count_limit =
243 ? (int) ((xvec_length + yvec_length) * (1.0 - lower_bound + 0.000001))
246 /* Now do the main comparison algorithm */
247 ctxt.edit_count = - ctxt.edit_count_limit;
248 if (compareseq (0, xvec_length, 0, yvec_length, 0, &ctxt))
249 /* The edit_count passed the limit. Hence the result would be
250 < lower_bound. We can return any value < lower_bound instead. */
252 ctxt.edit_count += ctxt.edit_count_limit;
255 ((number of chars in common) / (average length of the strings)).
257 = xvec_length - (number of calls to NOTE_DELETE)
258 = yvec_length - (number of calls to NOTE_INSERT)
259 = 1/2 * (xvec_length + yvec_length - (number of edits)).
260 This is admittedly biased towards finding that the strings are
261 similar, however it does produce meaningful results. */
262 return ((double) (xvec_length + yvec_length - ctxt.edit_count)
263 / (xvec_length + yvec_length));